The phase difference between displacement $x$ and velocity $v$ in SHM is:
A0
B$\pi/4$
C$\pi/2$ (velocity leads displacement by $\pi/2$)
D$\pi$
Answer & Solution
Correct answer: C. $\pi/2$ (velocity leads displacement by $\pi/2$)
$x = A\sin\omega t$ ⇒ $v = A\omega\cos\omega t = A\omega\sin(\omega t + \pi/2)$. So velocity leads displacement by $\pi/2$ (i.e., $v$ peaks 1/4 period earlier). Acceleration leads velocity by another $\pi/2$, so $a$ is $\pi$ out of phase with $x$.
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